FDM Line Width Formula
How FDM line width relates to nozzle diameter, layer height, and extrusion multiplier.
Covers cross-section geometry and the 100-125% width guideline.
Recommended Line Width
This is not a hard formula so much as a practical guideline. A 0.4mm nozzle works well at 0.40–0.50mm line width. Going below 100% forces the slicer to under-extrude relative to the nozzle bore, which creates gaps. Going above 150% asks the hotend to push plastic much wider than the nozzle diameter, which tends to cause poor surface finish and inconsistent extrusion.
Cross-Section Area
This is the stadium (oblong) cross-section approximation used in most slicers. The rectangular center has width (w-h) and height h; the two semicircular ends have radius h/2. Total area:
| Symbol | Meaning |
|---|---|
| A | Cross-sectional area of one deposited line (mm²) |
| w | Line width (mm) |
| h | Layer height (mm) |
Example
0.4mm nozzle, 0.45mm line width, 0.20mm layer height
A = (0.45 - 0.20) × 0.20 + π × (0.10)²
A = 0.25 × 0.20 + π × 0.01 = 0.05 + 0.0314
A = 0.0814 mm²
Compare to the circular filament cross-section: π × (0.875)² = 2.405 mm² for 1.75mm filament. Every 1mm of filament deposited produces 1/2.405 = 0.416 mm of line, so at 60 mm/s print speed you need 60 / 0.416 = 144 mm/s of filament feed speed from the extruder.
Key Notes
- Wider lines (0.6mm from a 0.4mm nozzle) print faster for the same coverage area but reduce fine detail resolution. Many users print perimeters at 0.45mm and infill at 0.6mm for speed without sacrificing surface quality.
- The extrusion multiplier (flow rate %) is a scalar applied to all extrusion moves. Setting it to 98% reduces all line widths by 2%. It is a correction factor, not a substitute for calibrating steps/mm.
- Variable line width (adaptive slicing, arachne perimeter generator) adjusts width mid-print to fill thin features without gaps. Prusaslicer and Orca Slicer both implement this. The cross-section formula still applies at each point; the width just varies along the path.